final_key - COT 3100-01 July, 26 2001 Final Exam (110...

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COT 3100-01 July, 26 2001 Final Exam (110 Total) Name:_________________ SSN:__________________ 1. Find the number of 8-letter passwords that can be formed by ordering the letters of the word DISCRETE subject to one of the following conditions. a) (5pts) Contain a substring EE. 7! b) (10 pts) Both E’s come after I . Here is one possible way to solve this problem. Letter I can occur in 1, 2, 3, 4, 5 and 6 position (from left to right). In accordance to this we can count separately 6 cases. Case 1: letter I in 1-st position. 7!/2! arrangements Case 2: letter I in the 2-nd position. Five choices (from letters D, S, C, T and R) for the 1-st position times 6!/2! (arrangements of 6 letters with 2 non- distinguishable). Case 3: letter I in the 3-rd position. For the first two positions preceding letter I we can choose from 5 letters, so there are 5 4 choices. This should be multiplies by 5!/2! Of the number of arrangements for the last 3 places. Case 4: letter I in the 4-th position: 5 4 3 choices for the preceding 3 positions and 4!/2! For the last two. Case 5: letter I in the 5-th position: 5 4 3 2 choices for the 4 first positions and 3!/2! Choices for the last three. Case 6: letter I in the 6-th position. 5! Choices for the first five positions and only
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final_key - COT 3100-01 July, 26 2001 Final Exam (110...

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